Are there any terms and conditions preventing me from setting up a minimal search form which POSTs to google? I.e. just a single text box with a 'search' button, that searches for pages on my site, via google. It doesn't seem likely that there would be anything preventing this, but the one thing that makes me wonder is the prevalence of branded google search with the 'www/my site' option, as used here (left sidebar).
It's legal, Google actually offers a free service that allows you to do so called Google Custom Search. It's free if you allow ads on your result page, if not, you'll have to pay for it. Check here.